Charge transport in disordered organic semiconductors is one of the key physical processes, responsible for the operation of organic electronic devices. The concept of the Gaussian Disorder Model (GDM) [1], i.e. the field-assisted and thermally-activated hopping of charge carriers in a spatially and energetically disordered manifold of transport sites distributed in energy in accord with the Gaussian law serves as the framework for the theoretical understanding of the hopping transport in disordered organics. The concept of transport level (or transport energy) in the framework of GDM is known to be a useful tool for analytic modeling, because it can greatly simplify the description of hopping transport by its reduction to the formalism of multiple trapping (MT) model [2-4]. The transport level is an analog of the mobility edge of the MT model. Both analytic and numerical modelling of a transport level has been based in general on the Miller-Abraham’s model for the hopping rates. Meanwhile, other models of hopping rates are in use, in particular – the Marcus model, which accounts for the polaron effect. Several variants of the transport level concept were introduced by different authors. In the present work, we show how the MT- description of hopping transport can be expanded beyond the Miller-Abraham’s model and even beyond the transport level concept.

Results of Monte-Carlo simulations of this work show that the escape time of a carrier from the rather deep state of energy E follows the exponential low, exp((E_C –E)/kT), for the rather broad energy interval, where E_C is the effective transport level, providing Marcus hopping rates. This result confirms an applicability of the effective transport level concept for the case of Marcus hopping rates.

Moreover, we develop the MT- formalism for the description of hopping transport, which is not including the transport level. Indeed, the distribution of “traps” has not the sharp upper boundary. The master equation of hopping transport reduced to the balance equation of MT model, irrespective to the use of a concrete model for the hopping rates between localized states (for example, the Miller-Abrahams or the Marcus model). One can apply this formalism for the non-stationary and spatially non-uniform problems. One can consider the well-known methods of transport level [2-4] and mean hopping parameter [5] as simplified and special versions of this formalism.